Modal Symbolic Learning: Appetizer¶

In [1]:
using Pkg
Pkg.activate(".")
Pkg.instantiate()
Pkg.update()
Pkg.status()
  Activating project at `~/Desktop/modal-symbolic-learning-course`
    Updating registry at `~/.julia/registries/General`
    Updating git-repo `https://github.com/JuliaRegistries/General.git`
  No Changes to `~/Desktop/modal-symbolic-learning-course/Project.toml`
  No Changes to `~/Desktop/modal-symbolic-learning-course/Manifest.toml`
Status `~/Desktop/modal-symbolic-learning-course/Project.toml`
  [a93c6f00] DataFrames v1.6.1
  [7806a523] DecisionTree v0.12.4
  [7073ff75] IJulia v1.24.2
  [033835bb] JLD2 v0.4.38
⌅ [add582a8] MLJ v0.19.5
  [c6f25543] MLJDecisionTreeInterface v0.4.0
  [e54bda2e] ModalDecisionTrees v0.3.3
  [91a5bcdd] Plots v1.39.0
  [7b3b3b3f] Sole v0.3.1
  [b002da8f] SoleLogics v0.6.12
  [4249d9c7] SoleModels v0.5.3
  [2913bbd2] StatsBase v0.34.2
  [9a3f8284] Random
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated`
In [2]:
# Import libraries for statistics & Machine Learning
using Random
using DataFrames
using MLJ
using Plots
In [3]:
# Import the Sole framework
using Sole

# Load an example time-series classification dataset as a tuple (DataFrame, Vector{String})
X, y = Sole.load_arff_dataset("NATOPS");
In [4]:
y
Out[4]:
360-element CategoricalArrays.CategoricalArray{String,1,UInt32}:
 "I have command"
 "I have command"
 "I have command"
 "I have command"
 "I have command"
 "I have command"
 "I have command"
 "I have command"
 "I have command"
 "I have command"
 "I have command"
 "I have command"
 "I have command"
 ⋮
 "Lock wings"
 "Lock wings"
 "Lock wings"
 "Lock wings"
 "Lock wings"
 "Lock wings"
 "Lock wings"
 "Lock wings"
 "Lock wings"
 "Lock wings"
 "Lock wings"
 "Lock wings"
In [5]:
X
Out[5]:
360×24 DataFrame
335 rows omitted
RowX[Hand tip l]Y[Hand tip l]Z[Hand tip l]X[Hand tip r]Y[Hand tip r]Z[Hand tip r]X[Elbow l]Y[Elbow l]Z[Elbow l]X[Elbow r]Y[Elbow r]Z[Elbow r]X[Wrist l]Y[Wrist l]Z[Wrist l]X[Wrist r]Y[Wrist r]Z[Wrist r]X[Thumb l]Y[Thumb l]Z[Thumb l]X[Thumb r]Y[Thumb r]Z[Thumb r]
Array…Array…Array…Array…Array…Array…Array…Array…Array…Array…Array…Array…Array…Array…Array…Array…Array…Array…Array…Array…Array…Array…Array…Array…
1[-0.519771, -0.52758, -0.531415, -0.517159, -0.510312, -0.518154, -0.50362, -0.485176, -0.466677, -0.444535 … -0.45501, -0.458937, -0.465048, -0.471251, -0.470015, -0.464627, -0.462666, -0.460253, -0.459572, -0.456737][-2.14011, -2.18043, -2.18425, -2.16547, -2.16635, -2.18836, -2.17162, -2.15248, -2.08072, -2.00607 … -2.17597, -2.1638, -2.17779, -2.17766, -2.17848, -2.16689, -2.15667, -2.13474, -2.13435, -2.13855][-0.957224, -0.970778, -0.970232, -0.960666, -0.962437, -0.970488, -0.966847, -0.96441, -0.972943, -0.979085 … -1.04234, -1.03616, -1.03756, -1.03275, -1.02525, -1.03115, -1.02558, -1.01884, -1.01701, -1.01059][0.675893, 0.699281, 0.673774, 0.700096, 0.765257, 0.980454, 1.43803, 1.78334, 2.08495, 2.32037 … 0.755717, 0.778103, 0.755128, 0.751274, 0.742517, 0.743311, 0.786792, 0.730863, 0.730482, 0.732217][-2.31794, -2.36398, -2.48698, -2.3176, -2.34228, -2.34828, -2.24596, -1.8102, -1.28214, -0.703666 … -2.45044, -2.33026, -2.44767, -2.43509, -2.44371, -2.42475, -2.25219, -2.38539, -2.38603, -2.35704][-0.254602, -0.246883, -0.252635, -0.235782, -0.13363, 0.051243, 0.078424, 0.274688, 0.335957, 0.390646 … -0.210761, -0.181256, -0.213764, -0.206785, -0.222643, -0.214863, -0.169845, -0.20958, -0.202703, -0.201438][-0.672175, -0.682166, -0.685415, -0.670036, -0.663511, -0.672929, -0.658353, -0.643332, -0.63439, -0.619762 … -0.627507, -0.629153, -0.633168, -0.634024, -0.635696, -0.63498, -0.633753, -0.632434, -0.634984, -0.633494][-0.811646, -0.826093, -0.826825, -0.820736, -0.821921, -0.831596, -0.82809, -0.823286, -0.806715, -0.791522 … -0.865485, -0.859529, -0.865397, -0.86135, -0.860462, -0.856847, -0.85257, -0.843446, -0.843199, -0.840282][-0.355687, -0.355521, -0.355221, -0.352447, -0.350348, -0.35277, -0.353647, -0.358977, -0.383944, -0.401975 … -0.419172, -0.41693, -0.417203, -0.414593, -0.414103, -0.412636, -0.412147, -0.411217, -0.410917, -0.410034][0.563137, 0.578847, 0.62441, 0.573098, 0.580253, 0.58863, 0.680733, 0.754091, 0.974406, 1.02492 … 0.545894, 0.506828, 0.50426, 0.496528, 0.494051, 0.491025, 0.487645, 0.478008, 0.474876, 0.47124][-0.844167, -0.86133, -1.01878, -0.833048, -0.835207, -0.858701, -0.991307, -0.937558, -0.774481, -0.674111 … -0.887136, -0.875202, -0.890925, -0.892577, -0.899166, -0.895402, -0.89024, -0.88102, -0.882138, -0.870535][0.049452, 0.059125, 0.129621, 0.046829, 0.049571, 0.062562, 0.154757, 0.290973, 0.335833, 0.368746 … -0.121716, -0.169222, -0.180047, -0.187447, -0.192183, -0.193964, -0.194436, -0.198232, -0.199414, -0.199562][-0.61342, -0.622232, -0.625402, -0.610388, -0.603729, -0.612568, -0.597349, -0.580095, -0.568276, -0.552699 … -0.546718, -0.550332, -0.556687, -0.559856, -0.561484, -0.560076, -0.558626, -0.556903, -0.558795, -0.557304][-1.61917, -1.65088, -1.65311, -1.6393, -1.64061, -1.65913, -1.64914, -1.62891, -1.57936, -1.53198 … -1.65347, -1.64678, -1.66345, -1.66018, -1.6606, -1.65403, -1.64625, -1.62997, -1.63138, -1.62842][-0.733924, -0.741974, -0.742438, -0.735815, -0.733838, -0.739854, -0.735757, -0.729296, -0.735961, -0.741818 … -0.808697, -0.804381, -0.807563, -0.803419, -0.802036, -0.798972, -0.796631, -0.791835, -0.792898, -0.792378][0.658217, 0.6748, 0.69276, 0.676511, 0.702911, 0.803806, 1.1038, 1.29536, 1.54963, 1.79337 … 0.716365, 0.698483, 0.702289, 0.697305, 0.697503, 0.696351, 0.709523, 0.68247, 0.679733, 0.676366][-1.78265, -1.8188, -1.96731, -1.78275, -1.7857, -1.79788, -1.76649, -1.4163, -1.10176, -0.69194 … -1.81824, -1.79328, -1.81183, -1.8076, -1.81251, -1.80468, -1.77535, -1.77539, -1.776, -1.75988][-0.084877, -0.077114, -0.090744, -0.07839, -0.006041, 0.083173, 0.208194, 0.298242, 0.319634, 0.336941 … -0.092348, -0.101278, -0.106751, -0.109804, -0.1102, -0.111331, -0.033403, -0.105637, -0.10567, -0.099408][-0.411614, -0.414309, -0.469108, -0.458497, -0.454544, -0.404415, -0.468829, -0.471275, -0.369598, -0.359469 … -0.340109, -0.345786, -0.349573, -0.353, -0.432727, -0.356777, -0.433848, -0.428835, -0.362735, -0.36165][-1.85323, -1.89515, -1.95368, -1.93915, -1.93447, -1.89835, -1.8739, -1.8562, -1.80774, -1.75773 … -1.9209, -1.92207, -1.92674, -1.92838, -1.94133, -1.90055, -1.93023, -1.90896, -1.87824, -1.87942][-0.865847, -0.866153, -1.00206, -0.997912, -0.994343, -0.870472, -0.971998, -0.985523, -0.850877, -0.851743 … -0.931213, -0.927843, -0.930593, -0.927086, -1.056, -0.907434, -1.07481, -1.063, -0.904668, -0.913975][0.567708, 0.589339, 0.580746, 0.58282, 0.615749, 0.95588, 1.40151, 1.67856, 1.88032, 2.07148 … 0.666981, 0.653051, 0.652106, 0.658308, 0.65612, 0.652261, 0.650332, 0.634315, 0.639449, 0.639242][-2.02875, -2.07658, -2.23551, -1.99931, -2.04665, -2.14399, -1.9481, -1.55118, -1.07181, -0.576404 … -2.20073, -2.099, -2.20651, -2.20833, -2.19677, -2.19554, -1.99028, -2.16158, -2.15648, -2.13581][-0.35898, -0.351665, -0.398628, -0.345991, -0.295307, -0.109899, 0.051552, 0.105771, 0.174518, 0.27263 … -0.340768, -0.331487, -0.367603, -0.343775, -0.342563, -0.34826, -0.264311, -0.354304, -0.337395, -0.326279]
2[-0.489753, -0.48607, -0.484529, -0.492771, -0.492031, -0.493076, -0.491979, -0.493256, -0.493156, -0.487527 … -0.400825, -0.414617, -0.407231, -0.397206, -0.366296, -0.354333, -0.371938, -0.386065, -0.408146, -0.415736][-1.55293, -1.54966, -1.55206, -1.55821, -1.556, -1.56055, -1.55812, -1.5648, -1.56414, -1.56731 … -1.6062, -1.62319, -1.61939, -1.6173, -1.58341, -1.5697, -1.55188, -1.54089, -1.52865, -1.52388][-0.907814, -0.911305, -0.92587, -0.921268, -0.928352, -0.928697, -0.932141, -0.930564, -0.933592, -0.932622 … -0.989828, -0.990365, -0.998319, -0.994962, -0.994991, -0.983351, -0.976952, -0.975923, -0.963954, -0.953944][0.632831, 0.633167, 0.637368, 0.640823, 0.635858, 0.63401, 0.634496, 0.637154, 0.640618, 0.643018 … 0.558287, 0.447356, 0.452128, 0.525122, 0.651756, 0.77637, 0.948441, 1.09432, 1.30458, 1.42438][-1.61526, -1.61763, -1.62374, -1.61861, -1.62068, -1.62244, -1.62164, -1.6257, -1.62654, -1.62966 … 1.56275, 1.58349, 1.59581, 1.60302, 1.55387, 1.53016, 1.47453, 1.47069, 1.45205, 1.39396][-0.63772, -0.637168, -0.644338, -0.651686, -0.653233, -0.654332, -0.651011, -0.6489, -0.654768, -0.653883 … 0.526364, 0.534895, 0.553634, 0.564454, 0.478762, 0.47897, 0.444671, 0.328608, 0.29968, 0.242647][-0.764322, -0.76326, -0.764375, -0.763831, -0.764855, -0.771226, -0.77035, -0.770268, -0.774302, -0.772458 … -0.673313, -0.688225, -0.68792, -0.684164, -0.670343, -0.661181, -0.660554, -0.6628, -0.667728, -0.670177][-0.450899, -0.450767, -0.452501, -0.454648, -0.455247, -0.452276, -0.453126, -0.454493, -0.452512, -0.454416 … -0.598891, -0.609533, -0.609361, -0.605956, -0.590388, -0.585079, -0.575719, -0.567138, -0.557045, -0.549239][-0.079976, -0.080762, -0.083669, -0.087223, -0.08914, -0.08982, -0.091631, -0.092721, -0.09304, -0.094382 … -0.18969, -0.186896, -0.185767, -0.185657, -0.184, -0.183172, -0.181486, -0.179875, -0.179443, -0.177455][0.588484, 0.588437, 0.591168, 0.595125, 0.594665, 0.594011, 0.594033, 0.595322, 0.594022, 0.595392 … 0.741419, 0.710198, 0.701785, 0.698899, 0.712752, 0.749419, 0.803343, 0.848877, 0.889374, 0.939079][-0.730616, -0.730755, -0.731663, -0.731757, -0.732705, -0.733491, -0.733443, -0.734938, -0.735328, -0.7363 … 0.603107, 0.620151, 0.630515, 0.62623, 0.614864, 0.587344, 0.54446, 0.511954, 0.400724, 0.336798][-0.013982, -0.014206, -0.017597, -0.023328, -0.024779, -0.023949, -0.023798, -0.023383, -0.023818, -0.023393 … 0.341478, 0.365238, 0.368656, 0.366911, 0.348588, 0.334984, 0.328527, 0.320669, 0.30213, 0.29275][-0.610917, -0.609945, -0.610197, -0.607995, -0.609012, -0.612652, -0.612659, -0.613082, -0.614878, -0.614069 … -0.53083, -0.549195, -0.54724, -0.54064, -0.518421, -0.502914, -0.500193, -0.503294, -0.516175, -0.523108][-1.03648, -1.03609, -1.03882, -1.03999, -1.04112, -1.03914, -1.04044, -1.04285, -1.04107, -1.0441 … -1.13693, -1.15922, -1.16127, -1.15574, -1.12468, -1.10677, -1.09263, -1.082, -1.07452, -1.06779][-0.577443, -0.578297, -0.583215, -0.588784, -0.591257, -0.591227, -0.593823, -0.596287, -0.595091, -0.597289 … -0.681441, -0.684264, -0.68352, -0.682579, -0.677352, -0.674626, -0.671057, -0.668541, -0.665837, -0.661711][0.659456, 0.659302, 0.662152, 0.665597, 0.665444, 0.665353, 0.665823, 0.667154, 0.665983, 0.667418 … 0.720035, 0.640724, 0.630026, 0.651852, 0.729677, 0.850068, 0.94295, 1.03751, 1.18761, 1.28357][-1.23593, -1.23487, -1.23632, -1.23402, -1.23438, -1.23515, -1.235, -1.23646, -1.23597, -1.23664 … 1.11925, 1.13986, 1.15143, 1.14894, 1.13129, 1.08879, 1.04614, 1.05516, 0.999333, 0.933612][-0.379883, -0.378978, -0.382435, -0.386875, -0.387906, -0.387474, -0.387414, -0.386467, -0.386541, -0.384717 … 0.361501, 0.393498, 0.396875, 0.391628, 0.364325, 0.331366, 0.325144, 0.324284, 0.307198, 0.269993][-0.635067, -0.633994, -0.633752, -0.648402, -0.648701, -0.632859, -0.640256, -0.64937, -0.649375, -0.640854 … -0.540383, -0.547009, -0.540366, -0.534912, -0.498297, -0.337868, -0.498095, -0.514231, -0.54187, -0.564004][-1.50539, -1.50707, -1.50899, -1.46215, -1.4642, -1.54008, -1.53225, -1.47132, -1.47094, -1.53011 … -1.57719, -1.59468, -1.59785, -1.61441, -1.57575, -1.43418, -1.52036, -1.51264, -1.50075, -1.4326][-0.846206, -0.845445, -0.853765, -0.831178, -0.836261, -0.844045, -0.849416, -0.846373, -0.847773, -0.848008 … -0.920237, -0.932154, -0.934714, -0.909785, -0.922902, -0.898096, -0.926457, -0.919174, -0.90991, -0.879849][0.447123, 0.44868, 0.45151, 0.449512, 0.449655, 0.44474, 0.448023, 0.453291, 0.451363, 0.454588 … 0.597487, 0.507611, 0.517329, 0.589425, 0.707242, 0.792697, 0.947473, 1.08187, 1.22891, 1.28773][-1.46324, -1.44853, -1.45427, -1.45388, -1.46205, -1.48701, -1.47933, -1.47592, -1.47542, -1.47576 … 1.42369, 1.4392, 1.43182, 1.45067, 1.4119, 1.40528, 1.38638, 1.28872, 1.19626, 1.1889][-0.547992, -0.537522, -0.542974, -0.561309, -0.569895, -0.593827, -0.586797, -0.579215, -0.582364, -0.580319 … 0.254432, 0.263169, 0.2516, 0.273131, 0.249835, 0.21509, 0.211921, 0.180549, 0.160028, 0.160106]
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⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮
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-0.327332, -0.327935, -0.326644, -0.325039, -0.3251, -0.30526 … -0.886368, -0.641939, -0.497255, -0.358087, -0.212964, -0.127756, -0.095887, -0.116937, -0.119397, -0.127444][0.509542, 0.50952, 0.509589, 0.51011, 0.510345, 0.510356, 0.510834, 0.512177, 0.51246, 0.512272 … 0.795192, 0.853224, 1.0132, 0.956989, 0.865689, 0.791048, 0.713106, 0.632409, 0.540583, 0.487938][-1.27347, -1.27437, -1.27418, -1.27142, -1.27255, -1.27315, -1.27045, -1.26474, -1.25445, -1.24991 … 0.003596, -0.31911, -0.660538, -0.908991, -1.12211, -1.23475, -1.30702, -1.34014, -1.4851, -1.37299][-0.702897, -0.703759, -0.704425, -0.702565, -0.70295, -0.703028, -0.699714, -0.693843, -0.687184, -0.683164 … -1.34799, -1.35434, -1.20712, -1.07756, -0.90488, -0.833757, -0.758002, -0.687452, -0.716255, -0.701383][-0.629855, -0.630139, -0.620592, -0.628961, -0.628939, -0.628438, -0.62663, -0.62448, -0.620829, -0.587977 … -0.447669, -0.618843, -0.713333, -0.809527, -0.802008, -0.768447, -0.7182, -0.717567, -0.66327, -0.649244][-1.53993, -1.54446, -1.59439, -1.52474, -1.51994, -1.53702, -1.53981, -1.53354, -1.53181, -1.52426 … -0.913601, -1.0781, -1.26635, -1.22622, -1.4285, -1.55837, -1.5881, -1.53614, -1.59409, -1.5352][-0.335227, -0.336029, -0.358805, -0.341048, -0.341273, -0.342193, -0.339988, -0.335084, -0.330522, -0.327064 … -1.19788, -1.01285, -0.988482, -0.642911, -0.522677, -0.456351, -0.398213, -0.191093, -0.164668, -0.116938][0.304616, 0.306086, 0.305318, 0.303448, 0.307583, 0.306656, 0.30791, 0.309052, 0.311916, 0.307903 … 0.786931, 0.8889, 0.968204, 0.953104, 0.818293, 0.73938, 0.617891, 0.591909, 0.501234, 0.534335][-1.4043, -1.36712, -1.39467, -1.39457, -1.38886, -1.39095, -1.38813, -1.37544, -1.35558, -1.373 … 0.039765, -0.34301, -0.74027, -1.06355, -1.3206, -1.51474, -1.52754, -1.66995, -1.65664, -1.53896][-0.807302, -0.805456, -0.809731, -0.813982, -0.805297, -0.807332, -0.803636, -0.799467, -0.791356, -0.794406 … -1.68142, -1.69987, -1.61319, -1.44354, -1.02504, -0.917653, -0.779174, -0.736609, -0.70255, -0.76388]
360[-0.553245, -0.551704, -0.548044, -0.544929, -0.546446, -0.546651, -0.554797, -0.580788, -0.634431, -0.679319 … -0.605506, -0.606554, -0.662612, -0.709257, -0.727722, -0.721847, -0.687693, -0.655425, -0.627145, -0.613324][-1.69493, -1.69349, -1.69951, -1.7085, -1.71117, -1.71164, -1.70638, -1.68895, -1.66512, -1.63018 … -1.76228, -1.75493, -1.74816, -1.73299, -1.72764, -1.72671, -1.725, -1.72086, -1.71081, -1.70149][-0.756008, -0.762863, -0.760376, -0.756736, -0.756973, -0.758584, -0.766189, -0.790081, -0.83163, -0.879984 … -0.568478, -0.590416, -0.601258, -0.618041, -0.641417, -0.648827, -0.660898, -0.674366, -0.687214, -0.689185][0.569726, 0.570003, 0.573506, 0.572164, 0.621714, 0.696098, 0.876118, 1.12203, 1.47091, 1.64837 … 0.503982, 0.51867, 0.550847, 0.56638, 0.586101, 0.585824, 0.581762, 0.575169, 0.572896, 0.568447][-1.8093, -1.80937, -1.80944, -1.80935, -1.8126, -1.85915, -1.8061, -1.67266, -1.36509, -1.061 … -1.84879, -1.81557, -1.82067, -1.82043, -1.8186, -1.8199, -1.81979, -1.8188, -1.81805, -1.81838][-0.448892, -0.45103, -0.445198, -0.449493, -0.440023, -0.397585, -0.392426, -0.419542, -0.481797, -0.566341 … -0.39616, -0.374028, -0.372259, -0.369527, -0.37349, -0.374199, -0.375562, -0.382328, -0.383967, -0.382463][-0.649971, -0.649416, -0.649301, -0.649405, -0.650603, -0.651655, -0.654168, -0.661633, -0.69253, -0.716346 … -0.622018, -0.617981, -0.63207, -0.64885, -0.661848, -0.666352, -0.665786, -0.659835, -0.651886, -0.64201][-0.661179, -0.661116, -0.660849, -0.660633, -0.660692, -0.660475, -0.658776, -0.654124, -0.641437, -0.63273 … -0.670818, -0.671412, -0.667998, -0.664196, -0.661352, -0.660271, -0.660424, -0.661436, -0.663717, -0.666132][-0.278644, -0.278702, -0.278181, -0.278777, -0.27941, -0.280517, -0.282926, -0.289208, -0.299268, -0.312043 … -0.210781, -0.206609, -0.207324, -0.212582, -0.219619, -0.2247, -0.230574, -0.23705, -0.239801, -0.244126][0.568073, 0.568343, 0.56841, 0.568293, 0.568819, 0.569378, 0.579864, 0.641647, 0.777616, 0.830986 … 0.551885, 0.547923, 0.549948, 0.552344, 0.554555, 0.557303, 0.559503, 0.56101, 0.562791, 0.564339][-0.778433, -0.778655, -0.778619, -0.778733, -0.779369, -0.780109, -0.779362, -0.766618, -0.717086, -0.682875 … -0.785922, -0.783846, -0.779921, -0.777165, -0.774594, -0.774036, -0.774061, -0.773732, -0.773823, -0.773722][-0.02143, -0.020536, -0.020128, -0.02009, -0.019628, -0.01872, -0.01719, -0.017495, -0.023465, -0.038239 … 0.010584, 0.02347, 0.024489, 0.023676, 0.021437, 0.020045, 0.019039, 0.017819, 0.017018, 0.016272][-0.628387, -0.62824, -0.627972, -0.62795, -0.628534, -0.629599, -0.634179, -0.643136, -0.690225, -0.722063 … -0.659737, -0.652085, -0.666734, -0.690343, -0.706105, -0.710851, -0.708535, -0.696575, -0.678107, -0.654597][-1.32808, -1.3284, -1.32776, -1.32786, -1.32877, -1.32952, -1.327, -1.31806, -1.27069, -1.24092 … -1.36105, -1.35757, -1.34966, -1.3408, -1.3366, -1.33417, -1.33318, -1.33293, -1.3339, -1.335][-0.596416, -0.595623, -0.595383, -0.595277, -0.595259, -0.595326, -0.59977, -0.612942, -0.646252, -0.662942 … -0.459595, -0.462904, -0.470229, -0.485661, -0.494149, -0.503453, -0.5141, -0.525152, -0.533987, -0.543757][0.596737, 0.596812, 0.59659, 0.596702, 0.600785, 0.649174, 0.739056, 0.887764, 1.1762, 1.26818 … 0.561642, 0.558598, 0.560472, 0.566841, 0.574092, 0.580397, 0.584519, 0.58644, 0.588266, 0.589908][-1.40353, -1.40435, -1.40359, -1.40375, -1.40652, -1.43477, -1.42129, -1.31078, -1.13539, -0.931755 … -1.4326, -1.41491, -1.41691, -1.41398, -1.41564, -1.41518, -1.41633, -1.41622, -1.41649, -1.41644][-0.288767, -0.288286, -0.287668, -0.287256, -0.285014, -0.279726, -0.260919, -0.248119, -0.303754, -0.336734 … -0.244798, -0.228921, -0.229544, -0.226317, -0.224749, -0.222938, -0.223814, -0.224805, -0.226123, -0.227229][-0.68502, -0.685204, -0.627984, -0.688225, -0.687581, -0.677684, -0.711667, -0.649013, -0.71614, -0.816832 … -0.693664, -0.725981, -0.756294, -0.732315, -0.803912, -0.796722, -0.76804, -0.551076, -0.523743, -0.546785][-1.4919, -1.49011, -1.53877, -1.48516, -1.4904, -1.53329, -1.39094, -1.56482, -1.53772, -1.3933 … -1.47424, -1.50293, -1.5229, -1.55835, -1.55701, -1.5713, -1.60818, -1.55696, -1.47954, -1.47578][-0.622853, -0.621667, -0.771939, -0.617503, -0.622762, -0.634211, -0.739624, -0.841439, -0.873699, -0.724369 … -0.438676, -0.476566, -0.503983, -0.70968, -0.535602, -0.552759, -0.56164, -0.60402, -0.62309, -0.74429][0.44287, 0.442447, 0.442904, 0.443035, 0.445075, 0.635029, 0.784021, 0.994775, 1.30717, 1.41446 … 0.560165, 0.587148, 0.516286, 0.606886, 0.581878, 0.547451, 0.546669, 0.548617, 0.542787, 0.532968][-1.59582, -1.55192, -1.55783, -1.61086, -1.5706, -1.8695, -1.64176, -1.65865, -1.3918, -1.11996 … -1.66752, -1.61219, -1.70301, -1.6115, -1.67477, -1.67718, -1.67334, -1.68026, -1.68111, -1.68382][-0.488496, -0.476734, -0.477444, -0.493527, -0.478055, -0.39622, -0.251282, -0.341591, -0.402661, -0.588205 … -0.367121, -0.342998, -0.262637, -0.307174, -0.282865, -0.239276, -0.240434, -0.248654, -0.251486, -0.253524]
In [6]:
# Let's inspect an instance for each class.
plot(map(i->plot(collect(X[i,:]), labels=nothing,title=y[i]), 1:30:180)..., layout = (2, 3), size = (1500,400))
Out[6]:
In [7]:
# *All* instances, grouped by class
plot(map(i->plot(collect.(eachrow(X[i:(i+30),:])), labels=nothing,title=y[i]), 1:30:180)..., layout = (2, 3), size = (1500,400))
Out[7]:
In [8]:
# Randomly split the data: 20% training, 80% testing
N = nrow(X)
perm = randperm(Random.MersenneTwister(1), N)
train_idxs, test_idxs = perm[1:round(Int, N*.2)], perm[round(Int, N*.2)+1:end];
println("Using $(length(train_idxs)) instances for training")
println("Using $(length(test_idxs)) instances for testing")
Using 72 instances for training
Using 288 instances for testing
In [9]:
DecisionTreeClassifier = @load DecisionTreeClassifier pkg=DecisionTree verbosity=0

# Instantiate the CART decision tree learning algorithm
model = DecisionTreeClassifier(;)
Out[9]:
DecisionTreeClassifier(
  max_depth = -1, 
  min_samples_leaf = 1, 
  min_samples_split = 2, 
  min_purity_increase = 0.0, 
  n_subfeatures = 0, 
  post_prune = false, 
  merge_purity_threshold = 1.0, 
  display_depth = 5, 
  feature_importance = :impurity, 
  rng = Random._GLOBAL_RNG())
In [10]:
# Bind data to learning algorithm
dt_mach = machine(model, X, y)

# Training fails!
@time fit!(dt_mach; rows=train_idxs)

report(dt_mach).print_tree()
┌ Warning: The number and/or types of data arguments do not match what the specified model
│ supports. Suppress this type check by specifying `scitype_check_level=0`.
│ 
│ Run `@doc DecisionTree.DecisionTreeClassifier` to learn more about your model's requirements.
│ 
│ Commonly, but non exclusively, supervised models are constructed using the syntax
│ `machine(model, X, y)` or `machine(model, X, y, w)` while most other models are
│ constructed with `machine(model, X)`.  Here `X` are features, `y` a target, and `w`
│ sample or class weights.
│ 
│ In general, data in `machine(model, data...)` is expected to satisfy
│ 
│     scitype(data) <: MLJ.fit_data_scitype(model)
│ 
│ In the present case:
│ 
│ scitype(data) = Tuple{Table{AbstractVector{AbstractVector{Continuous}}}, AbstractVector{Multiclass{6}}}
│ 
│ fit_data_scitype(model) = Tuple{Table{<:Union{AbstractVector{<:Continuous}, AbstractVector{<:Count}, AbstractVector{<:OrderedFactor}}}, AbstractVector{<:Finite}}
└ @ MLJBase ~/.julia/packages/MLJBase/ByFwA/src/machines.jl:230
[ Info: Training machine(DecisionTreeClassifier(max_depth = -1, …), …).
  3.864844 seconds (7.37 M allocations: 459.086 MiB, 5.06% gc time, 99.62% compilation time)
MethodError: no method matching round(::Vector{Float64}; sigdigits::Int64)

Closest candidates are:
  round(::Union{Float16, Float32, Float64}, ::RoundingMode{:ToZero}) got unsupported keyword argument "sigdigits"
   @ Base float.jl:392
  round(::Union{Float16, Float32, Float64}, ::RoundingMode{:Down}) got unsupported keyword argument "sigdigits"
   @ Base float.jl:393
  round(::Union{Float16, Float32, Float64}, ::RoundingMode{:Up}) got unsupported keyword argument "sigdigits"
   @ Base float.jl:394
  ...


Stacktrace:
 [1] #print_tree#109
   @ ~/.julia/packages/DecisionTree/0Dw1P/src/DecisionTree.jl:238 [inlined]
 [2] print_tree
   @ ~/.julia/packages/DecisionTree/0Dw1P/src/DecisionTree.jl:231 [inlined]
 [3] #print_tree#107
   @ ~/.julia/packages/DecisionTree/0Dw1P/src/DecisionTree.jl:198 [inlined]
 [4] print_tree(tree::DecisionTree.Root{Vector{Float64}, UInt32}, depth::Int64, indent::Int64; sigdigits::Int64, feature_names::Nothing)
   @ DecisionTree ~/.julia/packages/DecisionTree/0Dw1P/src/DecisionTree.jl:201
 [5] print_tree (repeats 2 times)
   @ ~/.julia/packages/DecisionTree/0Dw1P/src/DecisionTree.jl:200 [inlined]
 [6] (::MLJDecisionTreeInterface.TreePrinter{DecisionTree.Root{Vector{Float64}, UInt32}})()
   @ MLJDecisionTreeInterface ~/.julia/packages/MLJDecisionTreeInterface/cIWGa/src/MLJDecisionTreeInterface.jl:20
 [7] top-level scope
   @ In[10]:7
In [11]:
# All instances have the same length
length.(X)
Out[11]:
360×24 DataFrame
335 rows omitted
RowX[Hand tip l]Y[Hand tip l]Z[Hand tip l]X[Hand tip r]Y[Hand tip r]Z[Hand tip r]X[Elbow l]Y[Elbow l]Z[Elbow l]X[Elbow r]Y[Elbow r]Z[Elbow r]X[Wrist l]Y[Wrist l]Z[Wrist l]X[Wrist r]Y[Wrist r]Z[Wrist r]X[Thumb l]Y[Thumb l]Z[Thumb l]X[Thumb r]Y[Thumb r]Z[Thumb r]
Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64
1515151515151515151515151515151515151515151515151
2515151515151515151515151515151515151515151515151
3515151515151515151515151515151515151515151515151
4515151515151515151515151515151515151515151515151
5515151515151515151515151515151515151515151515151
6515151515151515151515151515151515151515151515151
7515151515151515151515151515151515151515151515151
8515151515151515151515151515151515151515151515151
9515151515151515151515151515151515151515151515151
10515151515151515151515151515151515151515151515151
11515151515151515151515151515151515151515151515151
12515151515151515151515151515151515151515151515151
13515151515151515151515151515151515151515151515151
⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮
349515151515151515151515151515151515151515151515151
350515151515151515151515151515151515151515151515151
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In [12]:
# Maybe let's unwind the temporal axis?
X_static = Matrix(X)
cols = []
for i_var in 1:size(X_static, 2)
    var_unroll = hcat(X_static[:,i_var]...)
    append!(cols, eachrow(var_unroll))
end
X_static = DataFrame(cols, ["$n[$i]" for n in names(X) for i in 1:51])
Out[12]:
360×1224 DataFrame
1124 columns and 335 rows omitted
RowX[Hand tip l][1]X[Hand tip l][2]X[Hand tip l][3]X[Hand tip l][4]X[Hand tip l][5]X[Hand tip l][6]X[Hand tip l][7]X[Hand tip l][8]X[Hand tip l][9]X[Hand tip l][10]X[Hand tip l][11]X[Hand tip l][12]X[Hand tip l][13]X[Hand tip l][14]X[Hand tip l][15]X[Hand tip l][16]X[Hand tip l][17]X[Hand tip l][18]X[Hand tip l][19]X[Hand tip l][20]X[Hand tip l][21]X[Hand tip l][22]X[Hand tip l][23]X[Hand tip l][24]X[Hand tip l][25]X[Hand tip l][26]X[Hand tip l][27]X[Hand tip l][28]X[Hand tip l][29]X[Hand tip l][30]X[Hand tip l][31]X[Hand tip l][32]X[Hand tip l][33]X[Hand tip l][34]X[Hand tip l][35]X[Hand tip l][36]X[Hand tip l][37]X[Hand tip l][38]X[Hand tip l][39]X[Hand tip l][40]X[Hand tip l][41]X[Hand tip l][42]X[Hand tip l][43]X[Hand tip l][44]X[Hand tip l][45]X[Hand tip l][46]X[Hand tip l][47]X[Hand tip l][48]X[Hand tip l][49]X[Hand tip l][50]X[Hand tip l][51]Y[Hand tip l][1]Y[Hand tip l][2]Y[Hand tip l][3]Y[Hand tip l][4]Y[Hand tip l][5]Y[Hand tip l][6]Y[Hand tip l][7]Y[Hand tip l][8]Y[Hand tip l][9]Y[Hand tip l][10]Y[Hand tip l][11]Y[Hand tip l][12]Y[Hand tip l][13]Y[Hand tip l][14]Y[Hand tip l][15]Y[Hand tip l][16]Y[Hand tip l][17]Y[Hand tip l][18]Y[Hand tip l][19]Y[Hand tip l][20]Y[Hand tip l][21]Y[Hand tip l][22]Y[Hand tip l][23]Y[Hand tip l][24]Y[Hand tip l][25]Y[Hand tip l][26]Y[Hand tip l][27]Y[Hand tip l][28]Y[Hand tip l][29]Y[Hand tip l][30]Y[Hand tip l][31]Y[Hand tip l][32]Y[Hand tip l][33]Y[Hand tip l][34]Y[Hand tip l][35]Y[Hand tip l][36]Y[Hand tip l][37]Y[Hand tip l][38]Y[Hand tip l][39]Y[Hand tip l][40]Y[Hand tip l][41]Y[Hand tip l][42]Y[Hand tip l][43]Y[Hand tip l][44]Y[Hand tip l][45]Y[Hand tip l][46]Y[Hand tip l][47]Y[Hand tip l][48]Y[Hand tip l][49]⋯
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In [13]:
# Bind data to learning algorithm
dt_mach_static = machine(model, X_static, y)

# Train!
@time fit!(dt_mach_static; rows=train_idxs);

report(dt_mach_static).print_tree()

# Compute accuracy
yhat = predict_mode(dt_mach_static; rows=test_idxs)
acc = MLJ.accuracy(yhat, y[test_idxs])
println("Accuracy: $(acc)")
[ Info: Training machine(DecisionTreeClassifier(max_depth = -1, …), …).
  0.830826 seconds (1.21 M allocations: 93.503 MiB, 2.64% gc time, 95.07% compilation time)
Feature 77 < -1.282 ?
├─ Feature 790 < 1.396 ?
    ├─ 3 : 12/12
    └─ Feature 499 < 1.055 ?
        ├─ Feature 1006 < -1.4 ?
            ├─ 1 : 16/16
            └─ 5 : 4/4
        └─ Feature 184 < 1.53 ?
            ├─ 3 : 1/1
            └─ 5 : 5/5
└─ Feature 380 < -0.02374 ?
    ├─ Feature 680 < -0.3382 ?
        ├─ 4 : 13/13
        └─ Feature 199 < 0.5233 ?
            ├─ 4 : 1/1
            └─ 6 : 7/7
    └─ Feature 525 < -0.07192 ?
        ├─ 2 : 12/12
        └─ 6 : 1/1
Accuracy: 0.5868055555555556
In [14]:
println(names(X_static)[73])
println(names(X_static)[790])
Y[Hand tip l][22]
X[Wrist r][25]
In [15]:
feature_importances(dt_mach_static)
Out[15]:
1224-element Vector{Pair{Symbol, Float64}}:
 Symbol("Y[Hand tip l][26]") => 0.3919728191493403
    Symbol("X[Wrist r][25]") => 0.15879837719523981
    Symbol("Y[Elbow l][23]") => 0.15430650160975126
    Symbol("Y[Wrist l][17]") => 0.08149246071839794
    Symbol("Y[Thumb l][37]") => 0.0787799819908887
    Symbol("X[Elbow r][40]") => 0.06189215649217878
    Symbol("Y[Elbow r][15]") => 0.02775124659197857
 Symbol("X[Hand tip r][46]") => 0.02372646104198667
 Symbol("X[Hand tip r][31]") => 0.02127999521023807
  Symbol("X[Hand tip l][1]") => 0.0
  Symbol("X[Hand tip l][2]") => 0.0
  Symbol("X[Hand tip l][3]") => 0.0
  Symbol("X[Hand tip l][4]") => 0.0
                             ⋮
    Symbol("Z[Thumb r][40]") => 0.0
    Symbol("Z[Thumb r][41]") => 0.0
    Symbol("Z[Thumb r][42]") => 0.0
    Symbol("Z[Thumb r][43]") => 0.0
    Symbol("Z[Thumb r][44]") => 0.0
    Symbol("Z[Thumb r][45]") => 0.0
    Symbol("Z[Thumb r][46]") => 0.0
    Symbol("Z[Thumb r][47]") => 0.0
    Symbol("Z[Thumb r][48]") => 0.0
    Symbol("Z[Thumb r][49]") => 0.0
    Symbol("Z[Thumb r][50]") => 0.0
    Symbol("Z[Thumb r][51]") => 0.0
In [16]:
X_mean = DataFrame(mean.(Matrix(X)), ["mean($n)" for n in names(X)])
Out[16]:
360×24 DataFrame
335 rows omitted
Rowmean(X[Hand tip l])mean(Y[Hand tip l])mean(Z[Hand tip l])mean(X[Hand tip r])mean(Y[Hand tip r])mean(Z[Hand tip r])mean(X[Elbow l])mean(Y[Elbow l])mean(Z[Elbow l])mean(X[Elbow r])mean(Y[Elbow r])mean(Z[Elbow r])mean(X[Wrist l])mean(Y[Wrist l])mean(Z[Wrist l])mean(X[Wrist r])mean(Y[Wrist r])mean(Z[Wrist r])mean(X[Thumb l])mean(Y[Thumb l])mean(Z[Thumb l])mean(X[Thumb r])mean(Y[Thumb r])mean(Z[Thumb r])
Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64
1-0.441529-1.99325-0.9744781.17753-1.135450.101361-0.613209-0.797228-0.4050380.718652-0.5651790.100446-0.542541-1.5226-0.7507851.00038-0.9212320.133409-0.370604-1.75155-0.8992831.0711-1.01009-0.0516195
2-0.433127-1.55045-0.9547420.927408-0.379828-0.286614-0.7199-0.501027-0.1342590.73385-0.2616330.125011-0.562838-1.06006-0.6321360.892088-0.327576-0.116493-0.573686-1.4986-0.87920.813487-0.371786-0.283973
3-0.514139-1.76206-0.6244030.702343-0.627035-1.09901-0.514674-0.746088-0.04072520.712884-0.422115-0.500343-0.533024-1.38463-0.4205840.718922-0.557678-0.913565-0.401014-1.55589-0.6514940.664029-0.605402-1.10558
4-0.54604-1.86853-0.7251271.08656-0.584427-0.479782-0.6895-0.74642-0.2281440.877668-0.409193-0.108008-0.636323-1.48666-0.5844351.01217-0.537976-0.346185-0.730508-1.66997-0.616141.0367-0.546088-0.477238
5-0.608619-1.7987-0.8270251.00417-0.43575-0.319617-0.702146-0.788696-0.3055680.8192-0.314165-0.0272344-0.667252-1.46293-0.6753270.949805-0.380799-0.227083-0.770188-1.64486-0.7536051.02711-0.382477-0.342483
6-0.452965-1.9987-1.011161.07126-1.064850.178981-0.660759-0.780783-0.4515470.71541-0.6019690.369429-0.5648-1.49562-0.8120620.913442-0.9111150.246524-0.629652-1.80679-0.9088881.0105-1.062850.166492
7-0.475165-2.09609-0.9413481.23749-0.9652240.275899-0.683104-0.817153-0.4101470.780974-0.665150.395884-0.597465-1.56819-0.7757461.06021-0.893680.293467-0.418622-1.80964-0.9224391.12936-0.9299210.208296
8-0.402244-1.79774-0.7064671.21315-0.449356-0.631085-0.538756-0.693987-0.1308410.921704-0.331958-0.182986-0.51433-1.36048-0.5136831.13443-0.400679-0.476162-0.312525-1.50874-0.7316531.13495-0.441984-0.643643
9-0.581116-1.75254-0.6181551.03402-0.639092-0.575176-0.611921-0.713442-0.08886760.859068-0.483007-0.0566167-0.66713-1.29546-0.3907951.01492-0.567729-0.350515-0.716923-1.50612-0.4689360.915153-0.576937-0.593327
10-0.483915-1.74924-0.7200241.33397-0.624704-0.452416-0.54399-0.700616-0.1798420.874849-0.379759-0.138082-0.52407-1.35246-0.5124431.17802-0.542814-0.351154-0.397916-1.54072-0.7233291.19036-0.525114-0.537482
11-0.611767-1.9223-0.7366760.991164-0.24062-0.796395-0.563634-0.797446-0.1588870.892275-0.314994-0.38916-0.612288-1.50433-0.5808350.99877-0.314781-0.672492-0.43971-1.69515-0.7573341.03626-0.294066-0.741488
12-0.595399-1.63924-0.8621691.19874-0.368009-0.177448-0.663887-0.678814-0.2427190.792181-0.191840.121218-0.670686-1.32286-0.6962131.04872-0.277322-0.0699145-0.607122-1.41822-0.8938391.11667-0.326273-0.230035
13-0.647034-1.87037-0.6284691.18445-0.731339-0.528762-0.653925-0.712748-0.03726820.917467-0.499303-0.0552-0.708103-1.41546-0.3956961.11847-0.642955-0.331228-0.530089-1.59898-0.6495481.03275-0.678406-0.505
⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮
349-0.528628-1.47935-0.8715920.871904-0.614831-0.473561-0.728204-0.706623-0.2561690.797255-0.502345-0.206722-0.623392-1.20068-0.6466670.889521-0.571311-0.393645-0.545033-1.29719-0.8221330.911729-0.56195-0.516098
350-0.391091-1.24245-0.6491910.429929-0.759488-0.773544-0.684957-0.615739-0.07727830.615303-0.485906-0.477473-0.551178-1.01866-0.4425440.518835-0.655888-0.697814-0.387767-1.09422-0.6221270.489042-0.701798-0.7677
351-0.294253-1.21454-0.8835260.727772-0.610082-0.284078-0.692342-0.664887-0.4555750.722325-0.532913-0.171167-0.445726-1.00317-0.7488420.758798-0.54726-0.273096-0.372756-1.14293-0.8267330.710812-0.525604-0.359432
352-0.149389-1.0713-0.8645210.560025-0.542136-0.61619-0.516076-0.646244-0.2461430.621417-0.34105-0.376579-0.323191-0.96587-0.6509190.617188-0.429769-0.58055-0.248622-0.997935-0.8071390.629294-0.460835-0.662836
353-0.423029-1.19482-1.047280.938631-0.554863-0.204354-0.680112-0.51714-0.1101990.752368-0.4089590.0156558-0.591194-0.881049-0.6191520.877732-0.509368-0.100999-0.444482-1.01915-0.9447730.92389-0.556141-0.294183
354-0.26923-1.38106-0.8716160.453254-0.792699-0.921229-0.549234-0.700655-0.1461160.567558-0.455335-0.498257-0.415451-1.16512-0.6044360.536696-0.63519-0.79227-0.326377-1.28203-0.7675280.445161-0.693487-0.89879
355-0.342298-1.4574-0.9503011.01039-0.930284-0.409856-0.680879-0.741757-0.3365370.781863-0.597116-0.174152-0.48298-1.1747-0.7294080.960872-0.791981-0.304143-0.424199-1.34825-0.8923710.999731-0.895871-0.367742
356-0.134113-1.10602-0.8244650.750383-0.467471-0.797686-0.542451-0.640251-0.2129680.679151-0.429163-0.451733-0.303869-0.944115-0.6003930.726963-0.433648-0.686361-0.213221-0.978798-0.7363670.770862-0.420895-0.798113
3570.097314-1.13352-1.009260.985647-0.620846-0.135043-0.507959-0.560256-0.5682980.767562-0.5611440.0294597-0.167547-0.958414-0.8269690.93904-0.590387-0.0565921-0.0612799-1.08553-0.8734880.973756-0.589152-0.22155
358-0.191882-1.13238-0.6800370.579504-0.473543-0.54315-0.667844-0.577705-0.2309820.691821-0.448703-0.357544-0.413-0.933812-0.5445580.664574-0.467982-0.497377-0.251071-0.95659-0.6675440.616339-0.464005-0.547947
359-0.323847-1.13138-0.8228450.649077-0.54487-0.887733-0.598337-0.692167-0.1382620.634919-0.410662-0.574469-0.450064-0.973081-0.5499270.662644-0.465592-0.786338-0.422863-1.04283-0.7016240.641082-0.511364-0.887887
360-0.196397-1.13002-0.8158920.803101-0.52948-0.374867-0.627403-0.557626-0.4109320.713302-0.510644-0.19534-0.38494-0.89961-0.6771540.776527-0.522018-0.312253-0.33815-1.01988-0.7250350.78377-0.524139-0.429422
In [17]:
# Bind data to learning algorithm
dt_mach_mean = machine(model, X_mean, y)

# Train!
@time fit!(dt_mach_mean; rows=train_idxs);

report(dt_mach_mean).print_tree()

# Compute accuracy
yhat = predict_mode(dt_mach_mean; rows=test_idxs)
acc = MLJ.accuracy(yhat, y[test_idxs])
println("Accuracy: $(acc)")
  0.012304 seconds (11.21 k allocations: 831.303 KiB, 89.54% compilation time)
Feature 20 < -1.249 ?
├─ Feature 23 < -0.7454 ?
    ├─ Feature 14 < -1.301 ?
        ├─ Feature 16 < 1.062 ?
            ├─ Feature 1 < -0.4752 ?
                ├─ 
                └─ 3 : 2/2
            └─ Feature 3 < -0.6793 ?
                ├─ 1 : 10/10
                └─ 
        └─ 5 : 4/4
    └─ Feature 1 < -0.3344 ?
        ├─ Feature 9 < -0.0677 ?
            ├─ 3 : 10/10
            └─ 5 : 1/1
        └─ 4 : 2/2
└─ Feature 20 < -0.9186 ?
    ├─ 4 : 11/11
    └─ Feature 11 < -0.4066 ?
        ├─ Feature 8 < -0.4618 ?
            ├─ Feature 4 < 0.7178 ?
                ├─ 2 : 1/1
                └─ 6 : 4/4
            └─ 2 : 11/11
        └─ Feature 19 < -0.448 ?
            ├─ 6 : 4/4
            └─ 4 : 1/1
Accuracy: 0.5625
[ Info: Training machine(DecisionTreeClassifier(max_depth = -1, …), …).
In [18]:
feature_importances(dt_mach_mean)
Out[18]:
24-element Vector{Pair{Symbol, Float64}}:
    Symbol("mean(Y[Thumb l])") => 0.4791426225511836
    Symbol("mean(Y[Thumb r])") => 0.11855588688427983
 Symbol("mean(Z[Hand tip l])") => 0.0750540336604416
 Symbol("mean(X[Hand tip l])") => 0.05539064800441363
    Symbol("mean(Y[Elbow l])") => 0.051129205956262525
    Symbol("mean(X[Wrist r])") => 0.047341464077600454
    Symbol("mean(Y[Elbow r])") => 0.047081868037396314
    Symbol("mean(Y[Wrist l])") => 0.04550508659728294
    Symbol("mean(X[Thumb l])") => 0.03472627003491997
    Symbol("mean(Z[Elbow l])") => 0.026377918698496972
 Symbol("mean(X[Hand tip r])") => 0.019694995497722176
 Symbol("mean(Y[Hand tip l])") => 0.0
 Symbol("mean(Y[Hand tip r])") => 0.0
 Symbol("mean(Z[Hand tip r])") => 0.0
    Symbol("mean(X[Elbow l])") => 0.0
    Symbol("mean(X[Elbow r])") => 0.0
    Symbol("mean(Z[Elbow r])") => 0.0
    Symbol("mean(X[Wrist l])") => 0.0
    Symbol("mean(Z[Wrist l])") => 0.0
    Symbol("mean(Y[Wrist r])") => 0.0
    Symbol("mean(Z[Wrist r])") => 0.0
    Symbol("mean(Z[Thumb l])") => 0.0
    Symbol("mean(X[Thumb r])") => 0.0
    Symbol("mean(Z[Thumb r])") => 0.0
In [19]:
X_features = DataFrame([
    eachcol(mean.(Matrix(X)))...,
    eachcol(maximum.(Matrix(X)))...,
    eachcol(minimum.(Matrix(X)))...,
], ["$f($n)" for n in names(X) for f in ["mean", "max", "min"]])
Out[19]:
360×72 DataFrame
335 rows omitted
Rowmean(X[Hand tip l])max(X[Hand tip l])min(X[Hand tip l])mean(Y[Hand tip l])max(Y[Hand tip l])min(Y[Hand tip l])mean(Z[Hand tip l])max(Z[Hand tip l])min(Z[Hand tip l])mean(X[Hand tip r])max(X[Hand tip r])min(X[Hand tip r])mean(Y[Hand tip r])max(Y[Hand tip r])min(Y[Hand tip r])mean(Z[Hand tip r])max(Z[Hand tip r])min(Z[Hand tip r])mean(X[Elbow l])max(X[Elbow l])min(X[Elbow l])mean(Y[Elbow l])max(Y[Elbow l])min(Y[Elbow l])mean(Z[Elbow l])max(Z[Elbow l])min(Z[Elbow l])mean(X[Elbow r])max(X[Elbow r])min(X[Elbow r])mean(Y[Elbow r])max(Y[Elbow r])min(Y[Elbow r])mean(Z[Elbow r])max(Z[Elbow r])min(Z[Elbow r])mean(X[Wrist l])max(X[Wrist l])min(X[Wrist l])mean(Y[Wrist l])max(Y[Wrist l])min(Y[Wrist l])mean(Z[Wrist l])max(Z[Wrist l])min(Z[Wrist l])mean(X[Wrist r])max(X[Wrist r])min(X[Wrist r])mean(Y[Wrist r])max(Y[Wrist r])min(Y[Wrist r])mean(Z[Wrist r])max(Z[Wrist r])min(Z[Wrist r])mean(X[Thumb l])max(X[Thumb l])min(X[Thumb l])mean(Y[Thumb l])max(Y[Thumb l])min(Y[Thumb l])mean(Z[Thumb l])max(Z[Thumb l])min(Z[Thumb l])mean(X[Thumb r])max(X[Thumb r])min(X[Thumb r])mean(Y[Thumb r])max(Y[Thumb r])min(Y[Thumb r])mean(Z[Thumb r])max(Z[Thumb r])min(Z[Thumb r])
Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64
1-0.441529-1.99325-0.9744781.17753-1.135450.101361-0.613209-0.797228-0.4050380.718652-0.5651790.100446-0.542541-1.5226-0.7507851.00038-0.9212320.133409-0.370604-1.75155-0.8992831.0711-1.01009-0.0516195-0.385018-1.6583-0.8815392.320371.444880.512204-0.554106-0.701578-0.3503481.167090.3472230.395771-0.491282-1.27806-0.6854481.793371.002030.406863-0.313351-1.46128-0.7805582.071481.368040.316459-0.531415-2.18836-1.057750.673774-2.48698-0.254602-0.685415-0.865485-0.4210550.47124-1.01878-0.199562-0.625402-1.66345-0.811140.658217-1.96731-0.111331-0.471275-1.95368-1.074810.567708-2.23551-0.398628
2-0.433127-1.55045-0.9547420.927408-0.379828-0.286614-0.7199-0.501027-0.1342590.73385-0.2616330.125011-0.562838-1.06006-0.6321360.892088-0.327576-0.116493-0.573686-1.4986-0.87920.813487-0.371786-0.283973-0.353775-1.47568-0.9078141.830051.603020.564454-0.645469-0.450767-0.0799761.164020.6305150.368656-0.490766-1.02786-0.5774431.600711.165670.396875-0.337868-1.41297-0.8230031.735991.450670.273131-0.493256-1.62319-0.9983190.447356-1.65607-0.663262-0.778831-0.609533-0.189690.588437-0.746939-0.02598-0.61691-1.16127-0.6842640.630026-1.25106-0.387906-0.652336-1.61441-0.9347140.44474-1.50104-0.644848
3-0.514139-1.76206-0.6244030.702343-0.627035-1.09901-0.514674-0.746088-0.04072520.712884-0.422115-0.500343-0.533024-1.38463-0.4205840.718922-0.557678-0.913565-0.401014-1.55589-0.6514940.664029-0.605402-1.10558-0.488133-1.72326-0.5741431.119671.10104-0.723884-0.500001-0.7262830.0050950.8944640.063335-0.317655-0.511855-1.31043-0.3243650.990010.671023-0.58639-0.374314-1.44806-0.5666631.006760.835528-0.787095-0.536751-1.80227-0.6595610.413413-1.81935-1.84328-0.535781-0.766074-0.0734730.57502-0.734555-0.786098-0.554929-1.43862-0.4723230.545204-1.4393-1.38572-0.481807-1.6696-0.708530.368699-1.59218-1.6821
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In [20]:
# Bind data to learning algorithm
dt_mach_features = machine(model, X_features, y)

# Train!
@time fit!(dt_mach_features; rows=train_idxs);

# report(dt_mach_features).print_tree()

# Compute accuracy
yhat = predict_mode(dt_mach_features; rows=test_idxs)
acc = MLJ.accuracy(yhat, y[test_idxs])
println("Accuracy: $(acc)")
  0.061459 seconds (151.81 k allocations: 10.587 MiB, 95.59% compilation time)
Accuracy: 0.6180555555555556
[ Info: Training machine(DecisionTreeClassifier(max_depth = -1, …), …).
In [21]:
feature_importances(dt_mach_features)
Out[21]:
72-element Vector{Pair{Symbol, Float64}}:
     Symbol("max(X[Wrist l])") => 0.39197281914934023
    Symbol("mean(Z[Thumb l])") => 0.18132225305149965
     Symbol("max(X[Elbow r])") => 0.16741068900972056
    Symbol("mean(Y[Thumb l])") => 0.06544665501303142
     Symbol("min(Z[Elbow l])") => 0.04649458245137583
     Symbol("min(Z[Wrist r])") => 0.028902043776759926
     Symbol("min(X[Thumb l])") => 0.02835735767872674
     Symbol("min(Y[Thumb l])") => 0.027751246591978564
     Symbol("min(Y[Wrist r])") => 0.024712997421798815
     Symbol("min(Y[Elbow r])") => 0.022598081318570353
     Symbol("min(Y[Thumb r])") => 0.015031274537197792
 Symbol("mean(X[Hand tip l])") => 0.0
  Symbol("max(X[Hand tip l])") => 0.0
                               ⋮
     Symbol("max(X[Thumb l])") => 0.0
     Symbol("max(Y[Thumb l])") => 0.0
     Symbol("max(Z[Thumb l])") => 0.0
     Symbol("min(Z[Thumb l])") => 0.0
    Symbol("mean(X[Thumb r])") => 0.0
     Symbol("max(X[Thumb r])") => 0.0
     Symbol("min(X[Thumb r])") => 0.0
    Symbol("mean(Y[Thumb r])") => 0.0
     Symbol("max(Y[Thumb r])") => 0.0
    Symbol("mean(Z[Thumb r])") => 0.0
     Symbol("max(Z[Thumb r])") => 0.0
     Symbol("min(Z[Thumb r])") => 0.0
In [22]:
using ModalDecisionTrees

# Instantiate the learning algorithm
mdt_model = ModalDecisionTree(; relations = :IA7);
In [23]:
# Bind data to learning algorithm
mach = machine(mdt_model, X, y)

# Train!
@time fit!(mach; rows=train_idxs)
[ Info: Precomputing logiset...
[ Info: Training machine(ModalDecisionTree(max_depth = nothing, …), …).
103.101365 seconds (888.51 M allocations: 46.521 GiB, 10.85% gc time, 44.55% compilation time)
Out[23]:
trained Machine; caches model-specific representations of data
  model: ModalDecisionTree(max_depth = nothing, …)
  args: 
    1:	Source @524 ⏎ Table{AbstractVector{AbstractVector{Continuous}}}
    2:	Source @155 ⏎ AbstractVector{Multiclass{6}}
In [24]:
# Compute accuracy
yhat = predict_mode(mach; rows=test_idxs)
MLJ.accuracy(yhat, y[test_idxs])
Out[24]:
0.7847222222222222
In [25]:
report(mach).printmodel(true; show_metrics = true)
▣ ⟨G⟩min[X[Hand tip l]] ≥ 0.428173
├✔ ⟨G⟩(min[X[Hand tip l]] ≥ 0.428173 ∧ ⟨G⟩min[X[Wrist l]] < -1.536833)
│├✔ ⟨G⟩(min[X[Hand tip l]] ≥ 0.428173 ∧ ⟨G⟩(min[X[Wrist l]] < -1.536833 ∧ ⟨A̅O̅⟩min[X[Hand tip l]] ≥ 0.428173))
││├✔ Spread wings : (ninstances = 8, confidence = 1.0, coverage = 1.0)
││└✘ Fold wings : (ninstances = 12, confidence = 1.0, coverage = 1.0)
│└✘ Lock wings : (ninstances = 14, confidence = 1.0, coverage = 1.0)
└✘ ⟨G⟩min[Y[Hand tip r]] ≥ 0.847021
 ├✔ I have command : (ninstances = 14, confidence = 0.93, coverage = 1.0)
 └✘ ⟨G⟩min[Z[Hand tip l]] ≥ -0.62357
  ├✔ ⟨G⟩(min[Z[Hand tip l]] ≥ -0.62357 ∧ min[Y[Hand tip r]] < -1.850843)
  │├✔ All clear : (ninstances = 4, confidence = 0.75, coverage = 1.0)
  │└✘ Not clear : (ninstances = 7, confidence = 1.0, coverage = 1.0)
  └✘ All clear : (ninstances = 13, confidence = 0.92, coverage = 1.0)

In [26]:
# Access model
tree = report(mach).model

# Extract the corresponding ruleset
ruleset = listrules(tree; use_shortforms = true);

# Print ruleset
printmodel.(ruleset; show_metrics = false, threshold_digits = 2, variable_names_map = [names(X)], parenthesize_atoms = true, hidemodality = true);
▣ ⟨G⟩((min[X[Hand tip l]] ≥ 0.43) ∧ ⟨G⟩((min[X[Wrist l]] < -1.54) ∧ ⟨A̅O̅⟩(min[X[Hand tip l]] ≥ 0.43)))  🠮  Spread wings

▣ ⟨G⟩((min[X[Hand tip l]] ≥ 0.43) ∧ ⟨G⟩(min[X[Wrist l]] < -1.54)) ∧ [G]((min[X[Hand tip l]] ≥ 0.43) → ([G]((min[X[Wrist l]] < -1.54) → ([A̅O̅](min[X[Hand tip l]] < 0.43)))))  🠮  Fold wings

▣ ⟨G⟩(min[X[Hand tip l]] ≥ 0.43) ∧ [G]((min[X[Hand tip l]] ≥ 0.43) → ([G](min[X[Wrist l]] ≥ -1.54)))  🠮  Lock wings

▣ ⟨G⟩(min[Y[Hand tip r]] ≥ 0.85) ∧ [G](min[X[Hand tip l]] < 0.43)  🠮  I have command

▣ ⟨G⟩((min[Z[Hand tip l]] ≥ -0.62) ∧ (min[Y[Hand tip r]] < -1.85)) ∧ [G](min[X[Hand tip l]] < 0.43) ∧ [G](min[Y[Hand tip r]] < 0.85)  🠮  All clear

▣ ⟨G⟩(min[Z[Hand tip l]] ≥ -0.62) ∧ [G](min[X[Hand tip l]] < 0.43) ∧ [G](min[Y[Hand tip r]] < 0.85) ∧ [G]((min[Z[Hand tip l]] ≥ -0.62) → (min[Y[Hand tip r]] ≥ -1.85))  🠮  Not clear

▣ [G](min[X[Hand tip l]] < 0.43) ∧ [G](min[Y[Hand tip r]] < 0.85) ∧ [G](min[Z[Hand tip l]] < -0.62)  🠮  All clear

In [27]:
first_rule = ruleset[1]
first_antd = antecedent(first_rule)

println("First formula, translated:")
println(SoleLogics.experimentals.formula2natlang(first_antd; threshold_digits = 2))

println()
println("All formulas, translated:")

for (i_rule, rule) in enumerate(ruleset)
    println()
    println("[$i_rule]")
    print("IF\t")
    antd = antecedent(rule)
    consq = consequent(rule)
    println(SoleLogics.experimentals.formula2natlang(antd; threshold_digits = 2));
    print("THEN\t")
    println(consq)
end
First formula, translated:
∃ interval where ((min[V1] ≥ 0.43) and (∃ interval where ((min[V13] < -1.54) and (∃ preceding, partially overlapping interval where (min[V1] ≥ 0.43)))))

All formulas, translated:

[1]
IF	∃ interval where ((min[V1] ≥ 0.43) and (∃ interval where ((min[V13] < -1.54) and (∃ preceding, partially overlapping interval where (min[V1] ≥ 0.43)))))
THEN	▣ Spread wings


[2]
IF	(∃ interval where ((min[V1] ≥ 0.43) and (∃ interval where (min[V13] < -1.54)))) and (∀ intervals (whenever min[V1] ≥ 0.43 holds, also ∀ intervals (whenever min[V13] < -1.54 holds, also ∀ preceding, partially overlapping intervals (min[V1] < 0.43))))
THEN	▣ Fold wings


[3]
IF	(∃ interval where (min[V1] ≥ 0.43)) and (∀ intervals (whenever min[V1] ≥ 0.43 holds, also ∀ intervals (min[V13] ≥ -1.54)))
THEN	▣ Lock wings


[4]
IF	(∃ interval where (min[V5] ≥ 0.85)) and (∀ intervals (min[V1] < 0.43))
THEN	▣ I have command


[5]
IF	((∃ interval where ((min[V3] ≥ -0.62) and (min[V5] < -1.85))) and (∀ intervals (min[V1] < 0.43))) and (∀ intervals (min[V5] < 0.85))
THEN	▣ All clear


[6]
IF	(((∃ interval where (min[V3] ≥ -0.62)) and (∀ intervals (min[V1] < 0.43))) and (∀ intervals (min[V5] < 0.85))) and (∀ intervals (whenever min[V3] ≥ -0.62 holds, also min[V5] ≥ -1.85))
THEN	▣ Not clear


[7]
IF	((∀ intervals (min[V1] < 0.43)) and (∀ intervals (min[V5] < 0.85))) and (∀ intervals (min[V3] < -0.62))
THEN	▣ All clear